Analysis in Integer and Fractional Dimensions (Cambridge by Ron Blei

This ebook presents an intensive and self-contained research of interdependence and complexity in settings of useful research, harmonic research and stochastic research. It makes a speciality of 'dimension' as a uncomplicated counter of levels of freedom, resulting in special family among combinatorial measurements and numerous indices originating from the classical inequalities of Khintchin, Littlewood and Grothendieck. the fundamental innovations of fractional Cartesian items and combinatorial measurement are brought and associated with scales calibrated by way of harmonic-analytic and stochastic measurements. issues contain the (two-dimensional) Grothendieck inequality and its extensions to raised dimensions, stochastic versions of Brownian movement, levels of randomness and Frechet measures in stochastic research. This ebook is essentially aimed toward graduate scholars specialising in harmonic research, useful research or likelihood idea. It includes many routines and is appropriate for use as a textbook. it's also of curiosity to scientists from different disciplines, together with laptop scientists, physicists, statisticians, biologists and economists.

The aim of this monograph is to provide the present prestige of a swiftly constructing a part of a number of complicated variables, stimulated via the applicability of powerful effects to algebraic geometry and differential geometry. Highlighted are the recent special effects at the L² extension of holomorphic services.

Small-radius tubular buildings have attracted substantial realization within the previous couple of years, and are often utilized in diverse components reminiscent of Mathematical Physics, Spectral Geometry and worldwide research. during this monograph, we examine Laplace-like operators on skinny tubular constructions ("graph-like spaces''), and their typical limits on metric graphs.

This obtainable monograph covers larger order linear and nonlinear elliptic boundary price difficulties in bounded domain names, in most cases with the biharmonic or poly-harmonic operator as best primary half. It presents speedy entry to contemporary effects and references.

This is often thesecondpart of the second one revised and prolonged variation ofthe good validated monograph approximately functionality areas. it's an advent to operate areas outlined when it comes to differentiability and integrability periods. It presents a listing of varied areas and merits as a guide if you use functionality areas to review different subject matters reminiscent of partial differential equations.